Find all pairs of consecutive even positive integers both of which are larger than 5 such that their sum is less than 23.

Find all pairs of consecutive even positive integers both of which are

1.	Find all pairs of consecutive even positive integers both of which are larger than 5 such that their sum is less than 23.
Answer» Let the required consecutive even integers be x and x + 2. Then, `xgt5 and x +(x+2)lt23` `rArrxgt5 and 2xlt21` `rArr 5ltx and x lt 10.5` `rArr 5 lt x lt 10.5` `therefore` x can take the even integral value 6, 8 and 10. Hence, the required pairs of even integers are (6, 8), (8, 10) and (10, 12).